ztrsna.f - Online Linux Manual Page

Section : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEztrsna.f
SYNOPSIS
Functions/Subroutinessubroutine ztrsna (JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, S, SEP, MM, M, WORK, LDWORK, RWORK, INFO)
ZTRSNA
Function/Subroutine Documentation
subroutine ztrsna (character JOB, character HOWMNY, logical, dimension( * ) SELECT, integer N, complex*16, dimension( ldt, * ) T, integer LDT, complex*16, dimension( ldvl, * ) VL, integer LDVL, complex*16, dimension( ldvr, * ) VR, integer LDVR, double precision, dimension( * ) S, double precision, dimension( * ) SEP, integer MM, integer M, complex*16, dimension( ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK, integer INFO)ZTRSNA Purpose: ZTRSNA estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary).Parameters: JOB JOB is CHARACTER*1 Specifies whether condition numbers are required for eigenvalues (S) or eigenvectors (SEP): = 'E': for eigenvalues only (S); = 'V': for eigenvectors only (SEP); = 'B': for both eigenvalues and eigenvectors (S and SEP).
HOWMNY HOWMNY is CHARACTER*1 = 'A': compute condition numbers for all eigenpairs; = 'S': compute condition numbers for selected eigenpairs specified by the array SELECT.
SELECT SELECT is LOGICAL array, dimension (N) If HOWMNY = 'S', SELECT specifies the eigenpairs for which condition numbers are required. To select condition numbers for the j-th eigenpair, SELECT(j) must be set to .TRUE.. If HOWMNY = 'A', SELECT is not referenced.
N N is INTEGER The order of the matrix T. N >= 0.
T T is COMPLEX*16 array, dimension (LDT,N) The upper triangular matrix T.
LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N).
VL VL is COMPLEX*16 array, dimension (LDVL,M) If JOB = 'E' or 'B', VL must contain left eigenvectors of T (or of any Q*T*Q**H with Q unitary), corresponding to the eigenpairs specified by HOWMNY and SELECT. The eigenvectors must be stored in consecutive columns of VL, as returned by ZHSEIN or ZTREVC. If JOB = 'V', VL is not referenced.
LDVL LDVL is INTEGER The leading dimension of the array VL. LDVL >= 1; and if JOB = 'E' or 'B', LDVL >= N.
VR VR is COMPLEX*16 array, dimension (LDVR,M) If JOB = 'E' or 'B', VR must contain right eigenvectors of T (or of any Q*T*Q**H with Q unitary), corresponding to the eigenpairs specified by HOWMNY and SELECT. The eigenvectors must be stored in consecutive columns of VR, as returned by ZHSEIN or ZTREVC. If JOB = 'V', VR is not referenced.
LDVR LDVR is INTEGER The leading dimension of the array VR. LDVR >= 1; and if JOB = 'E' or 'B', LDVR >= N.
S S is DOUBLE PRECISION array, dimension (MM) If JOB = 'E' or 'B', the reciprocal condition numbers of the selected eigenvalues, stored in consecutive elements of the array. Thus S(j), SEP(j), and the j-th columns of VL and VR all correspond to the same eigenpair (but not in general the j-th eigenpair, unless all eigenpairs are selected). If JOB = 'V', S is not referenced.
SEP SEP is DOUBLE PRECISION array, dimension (MM) If JOB = 'V' or 'B', the estimated reciprocal condition numbers of the selected eigenvectors, stored in consecutive elements of the array. If JOB = 'E', SEP is not referenced.
MM MM is INTEGER The number of elements in the arrays S (if JOB = 'E' or 'B') and/or SEP (if JOB = 'V' or 'B'). MM >= M.
M M is INTEGER The number of elements of the arrays S and/or SEP actually used to store the estimated condition numbers. If HOWMNY = 'A', M is set to N.
WORK WORK is COMPLEX*16 array, dimension (LDWORK,N+6) If JOB = 'E', WORK is not referenced.
LDWORK LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= 1; and if JOB = 'V' or 'B', LDWORK >= N.
RWORK RWORK is DOUBLE PRECISION array, dimension (N) If JOB = 'E', RWORK is not referenced.
INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal valueAuthor: Univ​. of Tennessee Univ​. of California Berkeley Univ​. of Colorado Denver NAG Ltd​. Date: November 2017 Further Details: The reciprocal of the condition number of an eigenvalue lambda is defined as S(lambda) = |v**H*u| / (norm(u)*norm(v)) where u and v are the right and left eigenvectors of T corresponding to lambda; v**H denotes the conjugate transpose of v, and norm(u) denotes the Euclidean norm. These reciprocal condition numbers always lie between zero (very badly conditioned) and one (very well conditioned). If n = 1, S(lambda) is defined to be 1. An approximate error bound for a computed eigenvalue W(i) is given by EPS * norm(T) / S(i) where EPS is the machine precision. The reciprocal of the condition number of the right eigenvector u corresponding to lambda is defined as follows. Suppose T = ( lambda c ) ( 0 T22 ) Then the reciprocal condition number is SEP( lambda, T22 ) = sigma-min( T22 - lambda*I ) where sigma-min denotes the smallest singular value. We approximate the smallest singular value by the reciprocal of an estimate of the one-norm of the inverse of T22 - lambda*I. If n = 1, SEP(1) is defined to be abs(T(1,1)). An approximate error bound for a computed right eigenvector VR(i) is given by EPS * norm(T) / SEP(i)Definition at line 251 of file ztrsna​.f​.
AuthorGenerated automatically by Doxygen for LAPACK from the source code​. 0
Johanes Gumabo
Data Size   :   24,201 byte
man-ztrsna.3Build   :   2025-03-22, 13:26   :  
Visitor Screen   :   x
Visitor Counter ( page / site )   :   2 / 1,209,403
Visitor ID   :     :  
Visitor IP   :   13.59.210.36   :  
Visitor Provider   :   AMAZON-02   :  
Provider Position ( lat x lon )   :   37.751000 x -97.822000   :   x
Provider Accuracy Radius ( km )   :   1000   :  
Provider City   :     :  
Provider Province   :   ,   :   ,
Provider Country   :   United States   :  
Provider Continent   :   North America   :  
Visitor Recorder   :   Version   :  
Visitor Recorder   :   Library   :  
Online Linux Manual Page   :   Version   :   Online Linux Manual Page - Fedora.40 - march=x86-64 - mtune=generic - 25.03.22
Online Linux Manual Page   :   Library   :   lib_c - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Online Linux Manual Page   :   Library   :   lib_m - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Data Base   :   Version   :   Online Linux Manual Page Database - 24.04.13 - march=x86-64 - mtune=generic - fedora-38
Data Base   :   Library   :   lib_c - 23.02.07 - march=x86-64 - mtune=generic - fedora.36
Very long time ago, I have the best tutor, Wenzel Svojanovsky. If someone knows the email address of Wenzel Svojanovsky, please send an email to johanesgumabo@gmail.com.
Help me, linux0001.com will expire on July 16, 2025. I have no money to renew it. View detail
If error, please print screen and send to johanes_gumabo@yahoo.co.id
Under development. Support me via PayPal.